A civil war is a war within a country. Lincoln’s decision to invade the Confederate States of America was not a war within one country.
the csa was never a nation. No real nation ever formally recognized their legitimacy.
Linmcoln viewed the war as civil, opposing traitors. The South insisted on the Commonwealth as a voluntary membership. The fixed membership of the Union prevailed.
Lincoln and most of the people in the Union disagreed. That disagreement was pretty much what the war was about.